A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Günter Last is Professor of Stochastics at the Karlsruhe Institute of Technology, Germany. He is a distinguished probabilist with particular expertise in stochastic geometry, point processes, and random measures. He coauthored a research monograph on marked point processes on the line as well as two textbooks on general mathematics. He has given many invited talks on his research worldwide.
Inhaltsangabe
Preface List of symbols 1. Poisson and other discrete distributions 2. Point processes 3. Poisson processes 4. The Mecke equation and factorial measures 5. Mappings, markings and thinnings 6. Characterisations of the Poisson process 7. Poisson processes on the real line 8. Stationary point processes 9. The Palm distribution 10. Extra heads and balanced allocations 11. Stable allocations 12. Poisson integrals 13. Random measures and Cox processes 14. Permanental processes 15. Compound Poisson processes 16. The Boolean model and the Gilbert graph 17. The Boolean model with general grains 18. Fock space and chaos expansion 19. Perturbation analysis 20. Covariance identities 21. Normal approximation 22. Normal approximation in the Boolean model Appendix A. Some measure theory Appendix B. Some probability theory Appendix C. Historical notes References Index.
Preface List of symbols 1. Poisson and other discrete distributions 2. Point processes 3. Poisson processes 4. The Mecke equation and factorial measures 5. Mappings, markings and thinnings 6. Characterisations of the Poisson process 7. Poisson processes on the real line 8. Stationary point processes 9. The Palm distribution 10. Extra heads and balanced allocations 11. Stable allocations 12. Poisson integrals 13. Random measures and Cox processes 14. Permanental processes 15. Compound Poisson processes 16. The Boolean model and the Gilbert graph 17. The Boolean model with general grains 18. Fock space and chaos expansion 19. Perturbation analysis 20. Covariance identities 21. Normal approximation 22. Normal approximation in the Boolean model Appendix A. Some measure theory Appendix B. Some probability theory Appendix C. Historical notes References Index.
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